A complex system such as a mobile robot can have many different states of operation, normal and faulty states; also, mobile robots must further deal with changing and noisy environment. The dynamics of a mobile robot in various states are often quite different. Nevertheless there is a need to monitor these systems online to determine their current state and take the appropriate action. Given the data available, we need to compute some kind of posterior probability distribution over the possible states, i.e. which is the most probable (faulty) state? We tackle the diagnosis problem by constructing a probability distribution over the states the mobile robot can be in. This distribution is updated as more observations arrive. The updating step is computationally infeasible, so we approximated this step using look-ahead Rao-Blackwellized Particle Filtering (la-RBPF) algorithm. La-RBPF's most important features are its low diagnosis error, low variance, and its ability to diagnose states having low prior probabilities. Early results are promising.